1. Field of the Invention
The present invention relates to an analysis method of analyzing discharge and an electric field of an apparatus.
2. Description of the Related Art
Image forming apparatuses, such as printers, copiers, and facsimile, using electrophotography have five processes including electrification, exposure, development, transfer, and cleaning.
The transfer process transfers a toner image formed on an image carrier to a transfer medium. In order to form a high-resolution image, it is desired to transfer the toner image to the transfer medium with higher transfer efficiency while suppressing toner spatter during the transfer. Accordingly, it is important to optimize various parameters, including the image carrier (photosensitive drum), the toner, the transfer medium, and transfer conditions.
Particularly, owing to popularization of color electrophotography, transfer methods using intermediate transfer members, such as intermediate transfer belts, are joining the mainstream in the transfer processes. In the transfer method using the intermediate transfer member, first, four-color toner images formed on the photosensitive member are sequentially superimposed and the superimposed toner image is subjected to primary transfer to the intermediate transfer belt. The images primarily transferred are finally and collectively subjected to secondary transfer to a final transfer medium, such as a transfer sheet, to form a final image. Accordingly, the two transfer processes are necessary to form the final image. In such a case, many parameters, including the photosensitive member, the toner, the intermediate transfer belt, the transfer sheet, and the transfer conditions in the primary and secondary transfer, are involved in the transfer efficiency in the two transfer processes.
Hitherto, the optimization of the various parameters in the transfer process has been mainly performed by experiment using, for example, a prototype apparatus. However, analysis using a computer also has come into use in recent years.
For example, a known technology calculates the electric potential distribution of a transfer apparatus in consideration of the current passing through the conductor, discharge, and the motion of an object. In this technology, a two-dimensional analysis area is divided into a plurality of small cells. A Poisson equation is used to calculate the electric potential of each cell by a finite difference method. The movement of the charge with the motion of, for example, the photosensitive drum or the intermediate transfer belt is calculated from the calculated electric potential distribution and the resistance of each member based on Ohm's law. The potential of each cell after the charge is moved is calculated, and the movement of the charge due to the discharge is calculated from the electric potential distribution based on Paschen's law and a capacitor theory. Repeating the cell division and the subsequent processes until the electric potential distribution becomes stable provides transfer electric field.
However, known technologies have the following problems.
Loose determination of an occurrence of the discharge is performed in the known technologies because the potential is defined at the center of each cell. In order to minimize the effect of the loose determination, it is necessary to divide the surface area of the object into small cells to calculate each value, thus requiring long calculation time.
In addition, since different methods of setting the discharge are used in different surface configuration of the object in the known technologies, specification for every simulation model is necessary and, therefore, an operator is required for complicated operation. Although the amount of electrostatic charge of the toner varies upon reception of the discharge, the discharge to the toner is not considered in the known technologies.
Since the known technologies use the theory of a capacitor having parallel electrodes to calculate the amount of charge that is moved due to the discharge, they are only applicable to a case in which the simulation model exhibits stratified material distribution having a uniform thickness in the direction of the electric line of force. Although the member, such as a static charge eliminator, using corona discharge is generally used in the transfer process, the analysis in consideration of the static charge eliminator is not discussed in the known technologies.
Furthermore, it is not possible to accurately reproduce the actual electric field distribution in the known technologies even when the calculation of the transfer electric field is performed.
It takes time for some materials used for, for example, the transfer rollers to exhibit dielectric polarization in response to the variation in the electric field. FIG. 24 is a graph schematically showing the variation in the amount of charge accumulated in electrodes with time when a step voltage is applied to a capacitor having parallel electrodes with the transfer roller sandwiched therebetween. Upon application of the voltage, charge Q1 is accumulated, the accumulated charge increases with time, and the charge remains constant at Q2. The charge decreases by the amount Q1 upon removal of the voltage, the charge gradually decreases with time, and finally falls into zero. Generally, the gradually increasing charge upon application of the voltage is called absorption charge and the gradually decreasing charge upon removal of the voltage is called residual charge. The curve of the absorption charge and the residual charge can be approximated by an exponential function. With respect to the material used for the transfer roller, the time constant of variation in the absorption charge and the residual charge is of the order of 0.1 seconds to several seconds. Such large time constant is caused by the long time until the material of the transfer roller exhibits the dielectric polarization.
This time constant is too large to be ignored, compared with the rotational speed of the transfer roller of a common electrophotographic apparatus. Specifically, a large electric field is generated near a nip on the transfer roller, whereas a small electric field is generated in the parts other than the nip. The large time constant of the dielectric polarization causes a phenomenon in which the dielectric polarization cannot catch up with the rotation of the transfer roller, which phenomenon has a large effect on the transfer performance.